Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <vector>
#include <cstdio>
using namespace std;

int n;
vector<double>v;

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		double tmp = 0;
		cin >> tmp;
		v.push_back(tmp);
	}
	double ans = -1.0;
	sort(v.begin(), v.end());
	for (int i = 1; i <= n-1; i++) {
		if (i == n-1) {
			double b = v[i] - v[i - 1];
			double s = v[i - 2] + v[i - 3];
			ans = max(ans, s / b);
		}
		else if (i == n - 2) {
			double b = v[i] - v[i - 1];
			double s = v[i + 1] + v[i - 2];
			ans = max(ans, s / b);
		}
		else {
			double b = v[i] - v[i - 1];
			double s = v[n - 1] + v[n - 2];
			ans = max(ans, s / b);
		}
	}
	printf("%.10f\n", ans);
}